Abstract:

Using Neumann series of inverse matrix,the discrete time algebraic Riccati matrix equation (DTARME) with unknown matrix inversion,which occurs in connection with the linear quadratic optimization problem,can be transformed into a highorder polynomial matrix equation.Then Newton’s method can be applied to find the symmetric solution to the highorder polynomial matrix equation.And from here,the modified conjugate gradient method can be used to find the symmetric solution or the symmetric leastsquare solution to the linear matrix equation derived from each iterative step of Newton's method.In this way,a double iterative algorithm is established to find the symmetric solution to DTARME.Having symmetric solution is the only requisite for DTARME based on the double iterative algorithm,and the solution may not necessarily be unique. Besides,there are no additional limits to the coefficient matrix of DTARME.Numerical experiments show that the double iterative algorithm is effective.

Key words: Riccati matrix equation;symmetric solution;Newton’s method;modified conjugate gradient method;double iterative algorithm